How To Get An Artifact Weapon

The first thing you are going to do when you begin your Legion experience after the events of the Broken Shore:

Seek out the Artifact for your spec

Follow your destiny and heed that calling to take up this ultimate weapon.

That experience going to vary depending on what class and what spec you play. For example

If you are a Retribution Paladin, you will returning to the location of the Broken Shore, to find and to seek out Ashbringer, were it fall in battle and is lost. So that you can take it up and wield it.

If you are a Protection Warrior, you will follow up on the legends of an ancient Vrykul king. Who was buried with a sword and shield, forged from the scales of the dragon Neltharion (Deathwing). You will delve into his tomb and overcome the ancient curse that lay there in order to wield those weapons for yourself.

If you are a Frost Deathknight, it will be the ultimate Frost Deathknight weapon Frostmourne. Frostmourne was shattered, but the first thing you are going to do is to go to Ice Crown Citadel and find and seek out the shards of the weapon after the battle with The Lich King. You will take those shards up and reforged them into a pair of rune blades.

As you level up, you gain experience and your character gains levels. But as you accomplish deeds in the world you will also earn artifact power for you weapon.